Subgroups — #552×Dic₄₇ #26376179

Order 12032.

2376 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246512	C₂	1	2	yes	maximal, complemented
2	#20246494	C₂	1	2	yes	maximal, complemented
3	#20246488	C₂	1	1	yes	maximal, characteristic, complemented
4	#20246419	C₂	1	1	yes	maximal, characteristic, complemented
5	#20246397	C₂	1	1	yes	maximal, characteristic, complemented
6	#20246384	C₂	1	2	yes	maximal
7	#20246353	C₂	1	1	yes	maximal, characteristic, complemented
8	#20246317	C₂	1	1	yes	maximal, characteristic
9	#20246273	C₂	1	1	yes	maximal, characteristic, complemented
10	#20246257	C₂	1	1	yes	maximal, characteristic, complemented
11	#20246248	C₂	1	2	yes	maximal, complemented
12	#125×Dic₄₇	C₂	1	2	yes	maximal, complemented
13	#125×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#126×Dic₄₇	C₂	1	2	yes	maximal, complemented
15	C₂²⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#123×Dic₄₇	C₂	1	2	yes	maximal
18	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
20	#117×Dic₄₇	C₂	1	2	yes	maximal, complemented
21	#117×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₇×#552	C₂	1	1	yes	maximal, characteristic
24	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×#13093983	C₂²	1	1	yes	characteristic
29	C₂×#13093983	C₂²	1	2	yes	—
30	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15689030	C₂²	1	1	yes	characteristic
35	#15689030	C₂²	1	1	yes	characteristic
36	#15689022	C₂²	1	1	yes	characteristic
37	#15689022	C₂²	1	1	yes	characteristic
38	#15689022	C₂²	1	2	yes	—
39	#15689022	C₂²	1	2	yes	—
40	#15689022	C₂²	1	1	yes	characteristic
41	#15689022	C₂²	1	1	yes	characteristic
42	#15689016	C₂²	1	2	yes	—
43	#15689016	C₂²	1	2	yes	—
44	#15689016	C₂²	1	2	yes	—
45	#15689016	C₂²	1	2	yes	—
46	#15689016	C₂²	1	2	yes	—
47	#15689009	C₂²	1	2	yes	—
48	#15689009	C₂²	1	2	yes	—
49	#15689009	C₂²	1	2	yes	—
50	#15689009	C₂²	1	2	yes	—
51	#15689009	C₂²	1	2	yes	—
52	#15689009	C₂²	1	2	yes	—
53	#15689009	C₂²	1	2	yes	—
54	#15689009	C₂²	1	2	yes	—
55	#15689009	C₂²	1	2	yes	—
56	#15689009	C₂²	1	2	yes	—
57	#15689009	C₂²	1	2	yes	—
58	#15689009	C₂²	1	2	yes	—
59	#15689009	C₂²	1	2	yes	—
60	#15689003	C₂²	1	2	yes	—
61	#15688998	C₂²	1	2	yes	—
62	#15688998	C₂²	1	2	yes	—
63	#15688998	C₂²	1	2	yes	—
64	#15688991	C₂²	1	2	yes	—
65	#15688989	C₂²	1	2	yes	—
66	#15688989	C₂²	1	1	yes	characteristic
67	#15688986	C₂²	1	2	yes	—
68	#15688983	C₂²	1	1	yes	characteristic
69	#15688983	C₂²	1	1	yes	characteristic
70	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
73	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
74	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
75	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
76	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
77	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
78	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
79	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
80	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
82	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
83	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
84	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
85	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
87	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
88	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
89	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
93	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
94	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
95	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
96	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
97	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
98	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
99	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
100	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
101	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
102	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
105	#15688969	C₂²	1	2	yes	—
106	#15688969	C₂²	1	2	yes	—
107	#15688969	C₂²	1	2	yes	—
108	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
109	C₄²×Dic₄₇	C₂²	1	2	yes	—
110	C₄²×Dic₄₇	C₂²	1	2	yes	—
111	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
112	C₄₇×#552	C₄	1	16	yes	complemented
113	C₂×#126×C₄₇	C₂²	1	2	yes	—
114	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
115	C₂×#125×C₄₇	C₂²	1	2	yes	—
116	C₂×#123×C₄₇	C₂²	1	2	yes	—
117	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
119	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
120	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
122	C₂×#117×C₄₇	C₂²	1	2	yes	—
123	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
124	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
125	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
126	C₂³×Dic₄₇	C₂³	1	2	yes	—
127	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
128	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
129	Q₈×Dic₄₇	—	2	4	no	—
130	Q₈×Dic₄₇	—	2	4	no	—
131	D₄×Dic₄₇	—	2	4	no	—
132	D₄×Dic₄₇	—	2	4	no	—
133	#13093983	—	2	8	no	—
134	#13093983	—	2	4	no	—
135	C₂×C₄⋊Dic₄₇	—	2	4	no	—
136	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
138	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
139	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
144	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
145	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
146	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
147	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
148	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×Dic₄₇	—	2	8	no	—
157	C₂×C₄×Dic₄₇	—	2	4	no	—
158	C₂×C₄×Dic₄₇	—	2	4	no	—
159	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
161	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
163	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
164	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
165	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
166	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
167	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
168	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
170	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
171	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
172	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
173	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
176	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
178	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
179	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
180	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
181	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
182	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
183	C₄₇⋊#95	C₂³	1	2	yes	—
184	C₄₇⋊#95	C₂³	1	2	yes	—
185	C₄₇⋊#95	C₂³	1	2	yes	—
186	C₄₇⋊#95	C₂³	1	2	yes	—
187	C₄₇⋊#95	C₂³	1	1	yes	characteristic
188	C₄₇⋊#95	C₂³	1	1	yes	characteristic
189	C₄₇⋊#95	C₂³	1	2	yes	—
190	C₄₇⋊#95	C₂³	1	2	yes	—
191	C₄₇⋊#95	C₂³	1	2	yes	—
192	C₄₇⋊#95	C₂³	1	2	yes	—
193	C₄₇⋊#95	C₂³	1	2	yes	—
194	C₄₇⋊#95	C₂³	1	2	yes	—
195	C₄₇⋊#95	C₂³	1	2	yes	—
196	C₄₇⋊#95	C₂³	1	2	yes	—
197	C₄₇⋊#95	C₂³	1	2	yes	—
198	C₄₇⋊#95	C₂³	1	1	yes	characteristic
199	C₄₇⋊#95	C₂³	1	1	yes	characteristic
200	C₄₇⋊#95	C₂³	1	1	yes	characteristic
201	C₄₇⋊#95	C₂³	1	1	yes	characteristic
202	C₄₇⋊#95	C₂³	1	2	yes	—
203	C₄₇⋊#95	C₂³	1	2	yes	—
204	C₄₇⋊#95	C₂³	1	2	yes	—
205	C₄₇⋊#95	C₂³	1	2	yes	—
206	C₄₇⋊#95	C₂³	1	2	yes	—
207	C₄₇⋊#95	C₂³	1	2	yes	—
208	C₄₇⋊#95	C₂³	1	2	yes	—
209	C₄₇⋊#95	C₂³	1	2	yes	—
210	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
211	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
213	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
215	#126×C₄₇	C₂×C₄	1	16	yes	complemented
216	#125×C₄₇	C₂×C₄	1	16	yes	complemented
217	#125×C₄₇	C₂×C₄	1	8	yes	complemented
218	#123×C₄₇	C₂×C₄	1	16	yes	—
219	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
220	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
221	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
222	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
223	#117×C₄₇	C₂×C₄	1	8	yes	complemented
224	#117×C₄₇	C₂×C₄	1	16	yes	complemented
225	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
239	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
241	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
242	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
243	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
244	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₄₇	—	2	2	no	—
247	C₂×Q₈×C₄₇	—	2	2	no	—
248	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
249	C₂×D₄×C₄₇	—	2	2	no	—
250	C₂×D₄×C₄₇	—	2	2	no	—
251	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₄₇	—	2	4	no	—
253	C₂²×C₄×C₄₇	—	2	4	no	—
254	C₂²×C₄×C₄₇	—	2	2	no	—
255	C₂²×C₄×C₄₇	—	2	2	no	—
256	C₂²×C₄×C₄₇	—	2	2	no	—
257	C₂²×C₄×C₄₇	—	2	2	no	—
258	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
259	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
260	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
261	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
270	C₂²×Dic₄₇	—	2	2	no	—
271	C₂²×Dic₄₇	—	2	2	no	—
272	C₂²×Dic₄₇	—	2	4	no	—
273	C₂²×Dic₄₇	—	2	2	no	—
274	C₂²×Dic₄₇	—	2	2	no	—
275	C₂²×Dic₄₇	—	2	2	no	—
276	C₂²×Dic₄₇	—	2	2	no	—
277	C₂²×Dic₄₇	—	2	4	no	—
278	C₂²×Dic₄₇	—	2	2	no	—
279	C₂²×Dic₄₇	—	2	2	no	—
280	C₂²×Dic₄₇	—	2	2	no	—
281	C₂²×Dic₄₇	—	4	1	no	—
282	C₂²×Dic₄₇	—	4	2	no	—
283	C₂²×Dic₄₇	—	4	1	no	—
284	C₂²×Dic₄₇	#41	1	4	yes	—
285	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
286	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
287	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
288	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
289	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
290	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
291	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
292	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
293	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
294	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
295	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
296	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
298	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
299	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
300	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
301	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
302	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
303	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
304	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
305	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
306	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
307	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
308	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
309	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
310	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
311	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
312	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
313	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
314	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
315	C₂²⋊Dic₄₇	—	2	4	no	—
316	C₂²⋊Dic₄₇	—	2	2	no	—
317	C₂²⋊Dic₄₇	—	2	4	no	—
318	C₂²⋊Dic₄₇	—	2	2	no	—
319	C₂²⋊Dic₄₇	—	2	2	no	—
320	C₂²⋊Dic₄₇	—	4	2	no	—
321	C₂²⋊Dic₄₇	#41	1	4	yes	—
322	C₄⋊Dic₄₇	—	2	2	no	—
323	C₄⋊Dic₄₇	—	2	2	no	—
324	C₄⋊Dic₄₇	—	2	2	no	—
325	C₄⋊Dic₄₇	—	2	4	no	—
326	C₄⋊Dic₄₇	—	2	4	no	—
327	C₄⋊Dic₄₇	—	2	4	no	—
328	C₄⋊Dic₄₇	—	2	2	no	—
329	C₄⋊Dic₄₇	—	2	2	no	—
330	C₄⋊Dic₄₇	—	2	4	no	—
331	C₄⋊Dic₄₇	—	2	4	no	—
332	C₄⋊Dic₄₇	—	4	2	no	—
333	C₄⋊Dic₄₇	—	4	2	no	—
334	C₄⋊Dic₄₇	#41	1	4	yes	—
335	C₄×Dic₄₇	—	2	2	no	—
336	C₄×Dic₄₇	—	2	2	no	—
337	C₄×Dic₄₇	—	2	2	no	—
338	C₄×Dic₄₇	—	2	4	no	—
339	C₄×Dic₄₇	—	2	2	no	—
340	C₄×Dic₄₇	—	2	4	no	—
341	C₄×Dic₄₇	—	2	2	no	—
342	C₄×Dic₄₇	—	2	4	no	—
343	C₄×Dic₄₇	—	2	2	no	—
344	C₄×Dic₄₇	—	2	4	no	—
345	C₄×Dic₄₇	—	2	2	no	—
346	C₄×Dic₄₇	—	2	4	no	—
347	C₄×Dic₄₇	—	2	4	no	—
348	C₄×Dic₄₇	—	2	4	no	—
349	C₄×Dic₄₇	—	2	2	no	—
350	C₄×Dic₄₇	—	2	2	no	—
351	C₄×Dic₄₇	—	2	4	no	—
352	C₄×Dic₄₇	—	2	4	no	—
353	C₄×Dic₄₇	—	2	2	no	—
354	C₄×Dic₄₇	—	2	4	no	—
355	C₄×Dic₄₇	—	4	2	no	—
356	C₄×Dic₄₇	—	4	2	no	—
357	C₄×Dic₄₇	—	4	1	no	—
358	C₄×Dic₄₇	#41	1	4	yes	—
359	C₂³×C₄₇	—	2	1	no	—
360	C₂³×C₄₇	—	2	1	no	—
361	C₂³×C₄₇	—	2	1	no	—
362	C₂³×C₄₇	—	2	1	no	—
363	C₂³×C₄₇	—	2	1	no	—
364	C₂³×C₄₇	—	2	1	no	—
365	C₂³×C₄₇	—	2	1	no	—
366	C₂³×C₄₇	—	2	1	no	—
367	C₂³×C₄₇	—	2	1	no	—
368	C₂³×C₄₇	—	2	1	no	—
369	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
370	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
371	C₂³×C₄₇	C₂×#41	1	2	yes	—
372	C₂³×C₄₇	C₂×#41	1	2	yes	—
373	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
374	Q₈×C₄₇	—	2	8	no	—
375	D₄×C₄₇	—	2	8	no	—
376	C₂×C₄×C₄₇	—	2	16	no	—
377	C₂×C₄×C₄₇	—	2	2	no	—
378	C₂×C₄×C₄₇	—	2	2	no	—
379	C₂×C₄×C₄₇	—	2	1	no	—
380	C₂×C₄×C₄₇	—	2	1	no	—
381	C₂×C₄×C₄₇	—	2	2	no	—
382	C₂×C₄×C₄₇	—	2	1	no	—
383	C₂×C₄×C₄₇	—	2	1	no	—
384	C₂×C₄×C₄₇	—	2	1	no	—
385	C₂×C₄×C₄₇	—	2	2	no	—
386	C₂×C₄×C₄₇	—	2	2	no	—
387	C₂×C₄×C₄₇	—	2	2	no	—
388	C₂×C₄×C₄₇	—	2	1	no	—
389	C₂×C₄×C₄₇	—	2	1	no	—
390	C₂×C₄×C₄₇	—	2	2	no	—
391	C₂×C₄×C₄₇	—	2	1	no	—
392	C₂×C₄×C₄₇	—	2	2	no	—
393	C₂×C₄×C₄₇	—	2	8	no	—
394	C₂×C₄×C₄₇	—	2	8	no	—
395	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
396	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
397	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
398	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
399	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
400	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
401	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
402	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
403	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
404	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
405	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
406	C₂×Dic₄₇	—	2	1	no	—
407	C₂×Dic₄₇	—	2	1	no	—
408	C₂×Dic₄₇	—	2	2	no	—
409	C₂×Dic₄₇	—	2	1	no	—
410	C₂×Dic₄₇	—	2	1	no	—
411	C₂×Dic₄₇	—	2	1	no	—
412	C₂×Dic₄₇	—	2	1	no	—
413	C₂×Dic₄₇	—	2	1	no	—
414	C₂×Dic₄₇	—	2	2	no	—
415	C₂×Dic₄₇	—	2	1	no	—
416	C₂×Dic₄₇	—	2	8	no	—
417	C₂×Dic₄₇	—	2	1	no	—
418	C₂×Dic₄₇	—	2	2	no	—
419	C₂×Dic₄₇	—	2	1	no	—
420	C₂×Dic₄₇	—	2	2	no	—
421	C₂×Dic₄₇	—	2	1	no	—
422	C₂×Dic₄₇	—	2	2	no	—
423	C₂×Dic₄₇	—	2	2	no	—
424	C₂×Dic₄₇	—	2	2	no	—
425	C₂×Dic₄₇	—	2	1	no	—
426	C₂×Dic₄₇	—	2	2	no	—
427	C₂×Dic₄₇	—	2	1	no	—
428	C₂×Dic₄₇	—	2	1	no	—
429	C₂×Dic₄₇	—	2	2	no	—
430	C₂×Dic₄₇	—	2	1	no	—
431	C₂×Dic₄₇	—	2	1	no	—
432	C₂×Dic₄₇	—	2	2	no	—
433	C₂×Dic₄₇	—	2	1	no	—
434	C₂×Dic₄₇	—	2	2	no	—
435	C₂×Dic₄₇	—	4	4	no	—
436	C₂×Dic₄₇	—	4	4	no	—
437	C₂×Dic₄₇	—	4	8	no	—
438	C₂×Dic₄₇	—	4	4	no	—
439	C₂×Dic₄₇	C₂×#41	1	2	yes	—
440	C₂×Dic₄₇	C₂×#41	1	2	yes	—
441	C₂×Dic₄₇	C₂×#41	1	2	yes	—
442	C₂×Dic₄₇	C₂×#41	1	2	yes	—
443	C₂×Dic₄₇	C₂×#41	1	4	yes	—
444	C₂×Dic₄₇	C₂×#41	1	2	yes	—
445	C₂×Dic₄₇	C₂×#41	1	2	yes	—
446	C₂×Dic₄₇	2₋¹⁺⁴	1	2	yes	—
447	C₄×#552	—	47	1	no	maximal, Sylow
448	C₂²×C₄₇	—	2	2	no	—
449	C₂²×C₄₇	—	2	2	no	—
450	C₂²×C₄₇	—	2	2	no	—
451	C₂²×C₄₇	—	2	2	no	—
452	C₂²×C₄₇	—	2	2	no	—
453	C₂²×C₄₇	—	2	2	no	—
454	C₂²×C₄₇	—	2	2	no	—
455	C₂²×C₄₇	—	2	2	no	—
456	C₂²×C₄₇	—	2	2	no	—
457	C₂²×C₄₇	—	4	1	no	—
458	C₂²×C₄₇	—	4	1	no	—
459	C₂²×C₄₇	—	4	1	no	—
460	C₂²×C₄₇	—	4	1	no	—
461	C₂²×C₄₇	C₄×#41	1	4	yes	—
462	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
463	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
464	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
466	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂²×C₄₇	#585	1	1	yes	characteristic
469	C₄×C₄₇	—	2	4	no	—
470	C₄×C₄₇	—	2	4	no	—
471	C₄×C₄₇	—	2	2	no	—
472	C₄×C₄₇	—	2	2	no	—
473	C₄×C₄₇	—	2	2	no	—
474	C₄×C₄₇	—	2	4	no	—
475	C₄×C₄₇	—	2	2	no	—
476	C₄×C₄₇	—	2	4	no	—
477	C₄×C₄₇	C₄×#41	1	4	yes	—
478	Dic₄₇	—	2	2	no	—
479	Dic₄₇	—	2	2	no	—
480	Dic₄₇	—	2	2	no	—
481	Dic₄₇	—	2	4	no	—
482	Dic₄₇	—	2	2	no	—
483	Dic₄₇	—	4	1	no	—
484	Dic₄₇	—	4	2	no	—
485	Dic₄₇	—	4	1	no	—
486	Dic₄₇	—	4	1	no	—
487	Dic₄₇	—	4	2	no	—
488	Dic₄₇	—	4	2	no	—
489	Dic₄₇	#552	1	4	yes	direct product factor
490	C₂×#552	D₄₇	1	1	yes	characteristic
491	#2373	—	47	2	no	—
492	#2371	—	47	2	no	—
493	#2370	—	47	1	no	—
494	#2362	—	47	1	no	—
495	#2360	—	47	1	no	—
496	#2359	—	47	2	no	—
497	#2356	—	47	1	no	—
498	#2352	—	47	1	no	—
499	#2346	—	47	1	no	—
500	#2344	—	47	1	no	—
501	#2343	—	47	2	no	—
502	C₄×#125	—	47	1	no	—
503	C₄×#125	—	47	2	no	—
504	C₄×#126	—	47	2	no	—
505	C₄×C₂²⋊Q₈	—	47	1	no	—
506	C₄×C₂²⋊Q₈	—	47	1	no	—
507	C₄×#123	—	47	2	no	—
508	C₄²×Q₈	—	47	1	no	—
509	C₄²×D₄	—	47	1	no	—
510	C₄×#117	—	47	2	no	—
511	C₄×#117	—	47	1	no	—
512	C₂×C₄×C₄⋊C₄	—	47	1	no	—
513	C₂×C₄₇	—	2	4	no	—
514	C₂×C₄₇	—	4	2	no	—
515	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
516	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
517	C₂×C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂×C₄₇	C₂×#552	1	1	yes	characteristic
519	C₂×C₄₇	#3475	1	1	yes	characteristic
520	C₂×C₄₇	#3475	1	1	yes	characteristic
521	C₂×C₄₇	#3482	1	1	yes	characteristic
522	#552	Dic₄₇	1	16	yes	direct product factor
523	C₂×#126	C₂×D₄₇	1	2	yes	—
524	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
525	C₂×#125	C₂×D₄₇	1	2	yes	—
526	C₂×#123	C₂×D₄₇	1	2	yes	—
527	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
528	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
529	C₂×C₄×Q₈	—	47	1	no	—
530	C₂×C₄×Q₈	—	47	1	no	—
531	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
532	C₂×C₄×D₄	—	47	1	no	—
533	C₂×C₄×D₄	—	47	1	no	—
534	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
535	C₂×#117	—	47	2	no	—
536	C₂×#117	—	47	1	no	—
537	C₂×#117	C₂×D₄₇	1	2	yes	—
538	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
539	C₂²×C₄⋊C₄	—	47	1	no	—
540	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
541	C₂²×C₄²	—	47	2	no	—
542	C₂²×C₄²	—	47	1	no	—
543	C₂²×C₄²	—	47	1	no	—
544	#391	—	47	1	no	—
545	#391	—	47	1	no	—
546	#389	—	47	1	no	—
547	#389	—	47	1	no	—
548	#389	—	47	2	no	—
549	#389	—	47	2	no	—
550	#389	—	47	1	no	—
551	#389	—	47	1	no	—
552	#388	—	47	2	no	—
553	#388	—	47	2	no	—
554	#388	—	47	2	no	—
555	#388	—	47	2	no	—
556	#388	—	47	2	no	—
557	#387	—	47	2	no	—
558	#387	—	47	2	no	—
559	#387	—	47	2	no	—
560	#387	—	47	2	no	—
561	#387	—	47	2	no	—
562	#387	—	47	2	no	—
563	#387	—	47	2	no	—
564	#387	—	47	2	no	—
565	#387	—	47	2	no	—
566	#387	—	47	2	no	—
567	#387	—	47	2	no	—
568	#387	—	47	2	no	—
569	#387	—	47	2	no	—
570	#386	—	47	2	no	—
571	#385	—	47	2	no	—
572	#385	—	47	2	no	—
573	#385	—	47	2	no	—
574	#383	—	47	2	no	—
575	#382	—	47	2	no	—
576	#382	—	47	1	no	—
577	#381	—	47	2	no	—
578	#380	—	47	1	no	—
579	#380	—	47	1	no	—
580	C₄×C₄⋊C₄	—	47	2	no	—
581	C₄×C₄⋊C₄	—	47	2	no	—
582	C₄×C₄⋊C₄	—	47	2	no	—
583	C₄×C₄⋊C₄	—	47	1	no	—
584	C₄×C₄⋊C₄	—	47	2	no	—
585	C₄×C₄⋊C₄	—	47	1	no	—
586	C₄×C₄⋊C₄	—	47	2	no	—
587	C₄×C₄⋊C₄	—	47	1	no	—
588	C₄×C₄⋊C₄	—	47	2	no	—
589	C₄×C₄⋊C₄	—	47	1	no	—
590	C₄×C₄⋊C₄	—	47	1	no	—
591	C₄×C₄⋊C₄	—	47	1	no	—
592	C₄×C₄⋊C₄	—	47	2	no	—
593	C₄×C₄⋊C₄	—	47	1	no	—
594	C₄×C₄⋊C₄	—	47	1	no	—
595	C₄×C₄⋊C₄	—	47	2	no	—
596	C₄×C₄⋊C₄	—	47	2	no	—
597	C₄×C₄⋊C₄	—	47	1	no	—
598	C₄×C₄⋊C₄	—	47	2	no	—
599	C₄×C₄⋊C₄	—	47	1	no	—
600	C₄×C₄⋊C₄	—	47	2	no	—
601	C₄×C₄⋊C₄	—	47	1	no	—
602	C₄×C₄⋊C₄	—	47	1	no	—
603	C₄×C₂²⋊C₄	—	47	1	no	—
604	C₄×C₂²⋊C₄	—	47	1	no	—
605	C₄×C₂²⋊C₄	—	47	1	no	—
606	C₄×C₂²⋊C₄	—	47	2	no	—
607	C₄×C₂²⋊C₄	—	47	2	no	—
608	C₄×C₂²⋊C₄	—	47	1	no	—
609	C₄×C₂²⋊C₄	—	47	2	no	—
610	C₄×C₂²⋊C₄	—	47	2	no	—
611	C₄×C₂²⋊C₄	—	47	2	no	—
612	C₄×C₂²⋊C₄	—	47	1	no	—
613	C₄×C₂²⋊C₄	—	47	1	no	—
614	C₄×C₂²⋊C₄	—	47	2	no	—
615	#376	—	47	2	no	—
616	#376	—	47	2	no	—
617	#376	—	47	2	no	—
618	C₂×#95	—	47	2	no	—
619	C₄³	—	47	2	no	—
620	C₄³	—	47	2	no	—
621	C₄³	—	47	1	no	—
622	C₄₇	C₄×#552	1	1	yes	characteristic, complemented, Sylow
623	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
624	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
625	C₂³×C₄	—	47	1	no	—
626	C₂³×C₄	—	47	1	no	—
627	C₂³×C₄	—	47	2	no	—
628	C₂³×C₄	—	47	1	no	—
629	C₂³×C₄	—	47	1	no	—
630	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
631	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
632	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
633	#126	C₂×Dic₄₇	1	16	yes	complemented
634	#125	C₂×Dic₄₇	1	16	yes	complemented
635	#125	C₂×Dic₄₇	1	8	yes	complemented
636	#123	C₂×Dic₄₇	1	16	yes	—
637	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
638	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
639	C₄×Q₈	—	94	4	no	—
640	C₄×Q₈	—	94	4	no	—
641	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
642	C₄×D₄	—	94	4	no	—
643	C₄×D₄	—	94	4	no	—
644	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
645	#117	—	94	8	no	—
646	#117	—	94	4	no	—
647	#117	C₂×Dic₄₇	1	8	yes	complemented
648	#117	C₂×Dic₄₇	1	16	yes	complemented
649	C₂×C₄⋊C₄	—	47	1	no	—
650	C₂×C₄⋊C₄	—	47	1	no	—
651	C₂×C₄⋊C₄	—	47	2	no	—
652	C₂×C₄⋊C₄	—	47	1	no	—
653	C₂×C₄⋊C₄	—	47	2	no	—
654	C₂×C₄⋊C₄	—	47	2	no	—
655	C₂×C₄⋊C₄	—	47	1	no	—
656	C₂×C₄⋊C₄	—	47	1	no	—
657	C₂×C₄⋊C₄	—	47	1	no	—
658	C₂×C₄⋊C₄	—	47	2	no	—
659	C₂×C₄⋊C₄	—	47	2	no	—
660	C₂×C₄⋊C₄	—	47	2	no	—
661	C₂×C₄⋊C₄	—	47	2	no	—
662	C₂×C₄⋊C₄	—	94	4	no	—
663	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
664	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
673	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
674	C₂×C₂²⋊C₄	—	47	1	no	—
675	C₂×C₂²⋊C₄	—	47	2	no	—
676	C₂×C₂²⋊C₄	—	47	2	no	—
677	C₂×C₂²⋊C₄	—	47	1	no	—
678	C₂×C₂²⋊C₄	—	47	1	no	—
679	C₂×C₂²⋊C₄	—	47	1	no	—
680	C₂×C₂²⋊C₄	—	47	2	no	—
681	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
686	C₂×C₄²	—	47	1	no	—
687	C₂×C₄²	—	47	2	no	—
688	C₂×C₄²	—	47	2	no	—
689	C₂×C₄²	—	47	2	no	—
690	C₂×C₄²	—	47	1	no	—
691	C₂×C₄²	—	47	1	no	—
692	C₂×C₄²	—	47	2	no	—
693	C₂×C₄²	—	47	1	no	—
694	C₂×C₄²	—	47	2	no	—
695	C₂×C₄²	—	47	1	no	—
696	C₂×C₄²	—	47	2	no	—
697	C₂×C₄²	—	47	1	no	—
698	C₂×C₄²	—	47	2	no	—
699	C₂×C₄²	—	47	1	no	—
700	C₂×C₄²	—	47	2	no	—
701	C₂×C₄²	—	47	1	no	—
702	C₂×C₄²	—	47	2	no	—
703	C₂×C₄²	—	47	1	no	—
704	C₂×C₄²	—	47	1	no	—
705	C₂×C₄²	—	47	1	no	—
706	C₂×C₄²	—	47	2	no	—
707	C₂×C₄²	—	47	1	no	—
708	C₂×C₄²	—	47	2	no	—
709	C₂×C₄²	—	47	2	no	—
710	C₂×C₄²	—	94	4	no	—
711	C₂×C₄²	—	94	4	no	—
712	C₂×C₄²	—	94	8	no	—
713	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
714	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
715	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
716	#95	—	47	2	no	—
717	#95	—	47	2	no	—
718	#95	—	47	2	no	—
719	#95	—	47	2	no	—
720	#95	—	47	1	no	—
721	#95	—	47	1	no	—
722	#95	—	47	2	no	—
723	#95	—	47	2	no	—
724	#95	—	47	2	no	—
725	#95	—	47	2	no	—
726	#95	—	47	2	no	—
727	#95	—	47	2	no	—
728	#95	—	47	2	no	—
729	#95	—	47	2	no	—
730	#95	—	47	2	no	—
731	#95	—	47	1	no	—
732	#95	—	47	1	no	—
733	#95	—	47	1	no	—
734	#95	—	47	1	no	—
735	#95	—	47	2	no	—
736	#95	—	47	2	no	—
737	#95	—	47	2	no	—
738	#95	—	47	2	no	—
739	#95	—	47	2	no	—
740	#95	—	47	2	no	—
741	#95	—	47	2	no	—
742	#95	—	47	2	no	—
743	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
744	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	47	1	no	—
758	C₂²×C₄	—	47	4	no	—
759	C₂²×C₄	—	47	1	no	—
760	C₂²×C₄	—	47	1	no	—
761	C₂²×C₄	—	47	1	no	—
762	C₂²×C₄	—	47	1	no	—
763	C₂²×C₄	—	47	2	no	—
764	C₂²×C₄	—	47	1	no	—
765	C₂²×C₄	—	47	2	no	—
766	C₂²×C₄	—	47	1	no	—
767	C₂²×C₄	—	47	2	no	—
768	C₂²×C₄	—	47	1	no	—
769	C₂²×C₄	—	47	2	no	—
770	C₂²×C₄	—	94	2	no	—
771	C₂²×C₄	—	94	2	no	—
772	C₂²×C₄	—	94	2	no	—
773	C₂²×C₄	—	94	2	no	—
774	C₂²×C₄	—	94	2	no	—
775	C₂²×C₄	—	94	4	no	—
776	C₂²×C₄	—	94	2	no	—
777	C₂²×C₄	—	94	2	no	—
778	C₂²×C₄	—	94	2	no	—
779	C₂²×C₄	—	94	4	no	—
780	C₂²×C₄	—	94	2	no	—
781	C₂²×C₄	—	188	1	no	—
782	C₂²×C₄	—	188	2	no	—
783	C₂²×C₄	—	188	1	no	—
784	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
785	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
786	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
787	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
789	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
790	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
791	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
792	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
793	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
794	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
796	C₄⋊C₄	—	47	4	no	—
797	C₄⋊C₄	—	94	4	no	—
798	C₄⋊C₄	—	94	4	no	—
799	C₄⋊C₄	—	94	4	no	—
800	C₄⋊C₄	—	94	2	no	—
801	C₄⋊C₄	—	94	2	no	—
802	C₄⋊C₄	—	94	4	no	—
803	C₄⋊C₄	—	94	4	no	—
804	C₄⋊C₄	—	94	2	no	—
805	C₄⋊C₄	—	94	2	no	—
806	C₄⋊C₄	—	94	2	no	—
807	C₄⋊C₄	—	188	2	no	—
808	C₄⋊C₄	—	188	2	no	—
809	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
810	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
811	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
812	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
813	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
814	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
815	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
816	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
817	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
818	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
819	C₂²⋊C₄	—	47	4	no	—
820	C₂²⋊C₄	—	94	4	no	—
821	C₂²⋊C₄	—	94	2	no	—
822	C₂²⋊C₄	—	94	2	no	—
823	C₂²⋊C₄	—	94	4	no	—
824	C₂²⋊C₄	—	94	2	no	—
825	C₂²⋊C₄	—	188	2	no	—
826	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
827	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
828	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
829	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
830	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
831	C₄²	—	47	4	no	—
832	C₄²	—	94	2	no	—
833	C₄²	—	94	4	no	—
834	C₄²	—	94	2	no	—
835	C₄²	—	94	2	no	—
836	C₄²	—	94	4	no	—
837	C₄²	—	94	4	no	—
838	C₄²	—	94	2	no	—
839	C₄²	—	94	2	no	—
840	C₄²	—	94	4	no	—
841	C₄²	—	94	4	no	—
842	C₄²	—	94	4	no	—
843	C₄²	—	94	4	no	—
844	C₄²	—	94	4	no	—
845	C₄²	—	94	2	no	—
846	C₄²	—	94	2	no	—
847	C₄²	—	94	4	no	—
848	C₄²	—	94	4	no	—
849	C₄²	—	94	2	no	—
850	C₄²	—	94	2	no	—
851	C₄²	—	94	2	no	—
852	C₄²	—	188	2	no	—
853	C₄²	—	188	1	no	—
854	C₄²	—	188	2	no	—
855	C₄²	C₂²×Dic₄₇	1	8	yes	—
856	C₄²	C₂²×Dic₄₇	1	8	yes	—
857	C₄²	C₂²×Dic₄₇	1	4	yes	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	C₂³×Dic₄₇	1	2	yes	—
869	C₂³	C₂³×Dic₄₇	1	2	yes	—
870	C₂³	#41×D₄₇	1	2	yes	—
871	C₂³	#41×D₄₇	1	2	yes	—
872	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
873	Q₈	—	2	8	no	—
874	D₄	—	2	8	no	—
875	C₂×C₄	—	2	16	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	47	2	no	—
895	C₂×C₄	—	47	2	no	—
896	C₂×C₄	—	47	2	no	—
897	C₂×C₄	—	47	2	no	—
898	C₂×C₄	—	47	2	no	—
899	C₂×C₄	—	47	2	no	—
900	C₂×C₄	—	47	2	no	—
901	C₂×C₄	—	47	4	no	—
902	C₂×C₄	—	94	8	no	—
903	C₂×C₄	—	94	1	no	—
904	C₂×C₄	—	94	1	no	—
905	C₂×C₄	—	94	1	no	—
906	C₂×C₄	—	94	2	no	—
907	C₂×C₄	—	94	1	no	—
908	C₂×C₄	—	94	1	no	—
909	C₂×C₄	—	94	1	no	—
910	C₂×C₄	—	94	1	no	—
911	C₂×C₄	—	94	2	no	—
912	C₂×C₄	—	94	1	no	—
913	C₂×C₄	—	94	1	no	—
914	C₂×C₄	—	94	1	no	—
915	C₂×C₄	—	94	2	no	—
916	C₂×C₄	—	94	1	no	—
917	C₂×C₄	—	94	2	no	—
918	C₂×C₄	—	94	2	no	—
919	C₂×C₄	—	94	2	no	—
920	C₂×C₄	—	94	2	no	—
921	C₂×C₄	—	94	1	no	—
922	C₂×C₄	—	94	1	no	—
923	C₂×C₄	—	94	1	no	—
924	C₂×C₄	—	94	2	no	—
925	C₂×C₄	—	94	2	no	—
926	C₂×C₄	—	94	1	no	—
927	C₂×C₄	—	94	2	no	—
928	C₂×C₄	—	94	1	no	—
929	C₂×C₄	—	94	2	no	—
930	C₂×C₄	—	94	1	no	—
931	C₂×C₄	—	188	4	no	—
932	C₂×C₄	—	188	4	no	—
933	C₂×C₄	—	188	4	no	—
934	C₂×C₄	—	188	8	no	—
935	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
936	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
937	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
938	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
939	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
940	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
941	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
942	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
943	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
944	C₂×C₄	#41×D₄₇	1	2	yes	—
945	C₂×C₄	#41×D₄₇	1	2	yes	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	#41×Dic₄₇	1	4	yes	—
960	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
961	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
962	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
963	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
964	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
965	C₂²	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
966	C₂²	#15689960	1	1	yes	characteristic
967	C₄	—	2	4	no	—
968	C₄	—	2	4	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	4	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	4	no	—
975	C₄	—	47	4	no	—
976	C₄	—	94	2	no	—
977	C₄	—	94	2	no	—
978	C₄	—	94	2	no	—
979	C₄	—	94	4	no	—
980	C₄	—	94	2	no	—
981	C₄	—	188	1	no	—
982	C₄	—	188	1	no	—
983	C₄	—	188	2	no	—
984	C₄	—	188	2	no	—
985	C₄	—	188	1	no	—
986	C₄	—	188	2	no	—
987	C₄	#41×Dic₄₇	1	4	yes	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
991	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
992	C₂	2₋¹⁺⁴×Dic₄₇	1	1	yes	characteristic
993	C₂	#552×D₄₇	1	1	yes	characteristic
994	C₂	#20256941	1	1	yes	characteristic
995	C₂	#20256953	1	1	yes	characteristic
996	C₂	#20257002	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#552	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂²×D₄×C₄₇	C₂³
hypercenter	C₂×#552	D₄₇
hypocenter	C₄₇	C₄×#552
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#552

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20246512	C₂	semidirect
2. #20246494	C₂	semidirect
3. #20246488	C₂	semidirect
4. #20246419	C₂	semidirect
5. #20246397	C₂	semidirect
7. #20246353	C₂	semidirect
9. #20246273	C₂	semidirect
10. #20246257	C₂	semidirect
11. #20246248	C₂	semidirect
12. #125×Dic₄₇	C₂	semidirect
13. #125×Dic₄₇	C₂	semidirect
14. #126×Dic₄₇	C₂	semidirect
15. C₂²⋊Q₈×Dic₄₇	C₂	semidirect
16. C₂²⋊Q₈×Dic₄₇	C₂	semidirect
18. C₄×Q₈×Dic₄₇	C₂	semidirect
20. #117×Dic₄₇	C₂	semidirect
21. #117×Dic₄₇	C₂	semidirect
22. C₂×C₄⋊C₄×Dic₄₇	C₂	semidirect
112. C₄₇×#552	C₄	semidirect
215. #126×C₄₇	C₂×C₄	semidirect
216. #125×C₄₇	C₂×C₄	semidirect
217. #125×C₄₇	C₂×C₄	semidirect
219. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
220. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
221. C₄×Q₈×C₄₇	C₂×C₄	semidirect
223. #117×C₄₇	C₂×C₄	semidirect
224. #117×C₄₇	C₂×C₄	semidirect
225. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
489. Dic₄₇	#552	direct (N × H)
522. #552	Dic₄₇	direct (N × H)
622. C₄₇	C₄×#552	semidirect
633. #126	C₂×Dic₄₇	semidirect
634. #125	C₂×Dic₄₇	semidirect
635. #125	C₂×Dic₄₇	semidirect
637. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
638. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
641. C₄×Q₈	C₂×Dic₄₇	semidirect
647. #117	C₂×Dic₄₇	semidirect
648. #117	C₂×Dic₄₇	semidirect
663. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20246512	2
#20246494	2
#20246488	2
#20246419	2
#20246397	2
#20246384	2
#20246353	2
#20246317	2
#20246273	2
#20246257	2
#20246248	2
#125×Dic₄₇	2
#126×Dic₄₇	2
C₂²⋊Q₈×Dic₄₇	2
#123×Dic₄₇	2
C₄×Q₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
#117×Dic₄₇	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄₇×#552	2
C₄×#552	47

Subgroups — #552×Dic47 #26376179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #552×Dic₄₇ #26376179